a) Assume that $\gamma$ is a symmetric convex curve w.r.t. two orthogonal lines (such a curve is the ellipse). Is the following statement true. There exists a $(l,L)$-bi-Lipschitz …

Edit: we cannot find such an example. It would imply a negative solution to the KS${}_2$ conjecture which has now been proven by Marcus, Spielman, and Srivastava in this paper. In …

A finite, two-player, nondegenerate, symmetric game is defined by a nondegenerate $n \times n$ payoff matrix $A$. If player 1 plays strategy $i$ and player 2 plays strategy $j$, t …

I believe the solution posted to the arXiv this morning by Marcus, Spielman, and Srivastava is correct. Apparently I am no longer able to accept answers, but if I could I would ac …

This question is inspired by a recent talk by Matt Kahle on random geometric complexes. Some simple notation: let $\mathcal{B} \subset \mathbb{R}^d$ be the unit ball in $d$-dimen …

Recall that a complex manifold is Stein if it is holomorphically convex and separable. If we assume holomorphically convex alone, then there is Cartan-Remmert reduction to say how …

Let $x_1,\ldots,x_N \in \{0,1\}^D$ be $N$ binary vectors, assumed affinely independent. Is there an efficient algorithm for determining whether a new binary vector $x_{N+1}$ is in …

Assume we have a real-analytic function $f(x, y)>0$ in some neighborhood of 0. When does there exist a complex-analytic function $w(z)$ such that $|w(z)|=f(x,y)$ for $z=x+iy$. One …

The Galvin-Prikry theorem says that Borel sets are Ramsey. This means that for every Borel set $S\subseteq[\omega]^\omega$, there is an $A\in[\omega]^\omega$ such that either $[A]^ …

For probably twenty years, category theorists have known of some objects in the Platonic universe called "(weak) $\infty$-categories", in which there are $k$-morphisms for all $k\i …

Let $R$ be a complete discrete valuation ring with maximal ideal $\mathfrak{p}$ and algebraically closed residue field $k$. Denote the field of fractions of $R$ by $F$. Let $G$ be …

There are many mathematical objects that are similar to groups and Cayley graphs of groups but lack homogeneity in some sense. Graphs of webpages with edges corresponding to links …

Let $G$ be a discrete group and let $M$ be a $G$-module. Assume that I have a resolution $$\cdots \rightarrow M_1 \rightarrow M_0 \rightarrow M \rightarrow 0$$ of $M$ by $G$-modul …

Let me begin with an example. Consider the computable function $f(x) = 2x$. A Turing machine can implement this function in $O(|n|)$ steps: simply walk to the end of the input st …

Let $G$ be a semisimple complex Lie group (or perhaps a reductive algebraic group over $\mathbb{C}$) and $V$ an irreducible finite-dimensional representation of $G$, determined by …